You are given \(v\) boolean variables \(x_0, x_1, ..., x_{v-1}\) that \(x_i\) can be either \(1\ (true)\) or \(0\ (false)\).
Let us define an environment \(env\), an assignment of either \(0\) or \(1\) to all \(v\) variables (like \(v=3,\ env = \{x_0=0, x_1=1, x_2=0\}\)).
Also, let us define an expression \(exp\), a string that can be generated by the following grammar:\(\langle expression \rangle ::= x_0\ |\ x_1\ |\ ...\ | x_{v-1}\ |\ \langle operation \rangle \\ \langle operation \rangle ::= (not\ \langle expression \rangle) \\ |\ (\langle expression \rangle\ and\ \langle expression \rangle) \\ |\ (\langle expression \rangle\ or\ \langle expression \rangle) \\ |\ (\langle expression \rangle\ xor\ \langle expression \rangle)\)

For example, is an expression.
Each expression has a value in an environment. (for example, expression \(((x_0\ xor\ x_1)\ or\ x_2)\) has value \(0\) in environment \(\{x_0=1, x_1=1, x_2=0\}\) but it has value \(1\) in environment \(\{x_0=0, x_1=0, x_2=1\}\) ).

You are given \(n\) environments \(env_1, env_2, ..., env_n\) and their expected value \(y_1, y_2, ..., y_n\) (the value that the expressions should have in them), find an expression that satisfies environments as much as possible, and uses operations (and, or, not, xor) as least as possible, in other words for each of \(20\) tests your score will be:

Let \(exp\) be your expression.
Let \(cnt\) be the number of environments like \(env_i\) that \(exp\ in\ env_i = y_i\).
\(score = \frac {e^{(\frac{cnt}{n})^2}-1}{e-1} \times (1 - \frac{number\ of\ used\ oprations}{1.5 \times n \times v}) \times 5\)

Input format

The first line contains two integers \(v\) and \(n\) separated by space.
Each of the following \(n\) lines contains space-separated \(env_i\) and \(y_i\), \(env_i\) is a string containing \(0\) and \(1\)s of length \(v\), the \(j^{th}\) character in \(env_i\) is value of \(v_j\) in \(env_i\).

Output format

Print a single line of the expression.

Constraints

\(1 \le n \le 100\)
In 7 tests: \(7 \le v \le 10\)
In 3 tests: \(10 < v \le 20\)
In other tests: \(30 \le v \le 50\)

Notes

The expression should not contain any space.
Print \(i\) instead of \(x_i\).
Print following characters instead of operations:
- & for \(and \).
- | for \(or \).
- ! for \(not\).
- ^ for \(xor\).
For example, \(((x_2\ xor\ (not\ x_1))\ or\ x_0)\) should be printed as \(((2^{!1})|0)\).
You can use at most \(1.5 \times n \times v\) operations.
The expression's length can be at most \(3 \times 10^4\).